T modity convenience yields. Convenience yield refers to the inverse carrying charges or return implied when spot prices plus storage costs and interest charges exceed the futures prices, holding risk considerations aside. An analytic expression for the convenience yield is derived in a market setting where temporary shocks to demand (or supply) can arise between the time when a futures contract is written and when that contract delivers. In this setting there may be an advantage to a position in inventory in meeting unexpected demand. Such an advantage, if it exists, is reflected in the relationship between equilibrium spot and futures prices, and may partially explain a negative basis (or contango) in seasonal commodities.
The intuition that holding the commodity in inventory provides an option not available from a futures contract is well documented. Kaldor (1939) and Working (1948) discuss this intuition and it is restated in the more recent empirical work of Brennan (1986) and Fama and French (1987). These recent articles empirically examine the 'theory of storage'. Brennan (1986) tests several empirical convenience yield models and finds that convenience yield is negatively related to inventory levels. Fama and French (1987) find that seasonalities are significant in explaining agricultural commodities' futures basis. They suggest that this seasonality is due to inventory fluctuations.'
The model developed here formalizes the empirical fact that inventory and convenience yield are negatively related, and demonstrates two new factors that influ-The authors would like to thank Rex Thompson, Margaret Slade, Alan Kraus, Josef Zechner, and, especially, Jim Brander for their many useful comments and suggestions. 'A recent article by Bresnahan and Spiller (1986) discusses the role of 'price shocks' on normal backwardation in futures markets. The model does not point out the option feature directly, nor does it draw out testable hypotheses, such as the relations of convenience yield to inventories or marginal production costs.